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Simplifying 0 = 5x2 + 13x + -7 Reorder the terms: 0 = -7 + 13x + 5x2 Solving 0 = -7 + 13x + 5x2 Solving for variable 'x'. Combine like terms: 0 + 7 = 7 7 + -13x + -5x2 = -7 + 13x + 5x2 + 7 + -13x + -5x2 Reorder the terms: 7 + -13x + -5x2 = -7 + 7 + 13x + -13x + 5x2 + -5x2 Combine like terms: -7 + 7 = 0 7 + -13x + -5x2 = 0 + 13x + -13x + 5x2 + -5x2 7 + -13x + -5x2 = 13x + -13x + 5x2 + -5x2 Combine like terms: 13x + -13x = 0 7 + -13x + -5x2 = 0 + 5x2 + -5x2 7 + -13x + -5x2 = 5x2 + -5x2 Combine like terms: 5x2 + -5x2 = 0 7 + -13x + -5x2 = 0 Begin completing the square. Divide all terms by -5 the coefficient of the squared term: Divide each side by '-5'. -1.4 + 2.6x + x2 = 0 Move the constant term to the right: Add '1.4' to each side of the equation. -1.4 + 2.6x + 1.4 + x2 = 0 + 1.4 Reorder the terms: -1.4 + 1.4 + 2.6x + x2 = 0 + 1.4 Combine like terms: -1.4 + 1.4 = 0.0 0.0 + 2.6x + x2 = 0 + 1.4 2.6x + x2 = 0 + 1.4 Combine like terms: 0 + 1.4 = 1.4 2.6x + x2 = 1.4 The x term is 2.6x. Take half its coefficient (1.3). Square it (1.69) and add it to both sides. Add '1.69' to each side of the equation. 2.6x + 1.69 + x2 = 1.4 + 1.69 Reorder the terms: 1.69 + 2.6x + x2 = 1.4 + 1.69 Combine like terms: 1.4 + 1.69 = 3.09 1.69 + 2.6x + x2 = 3.09 Factor a perfect square on the left side: (x + 1.3)(x + 1.3) = 3.09 Calculate the square root of the right side: 1.757839583 Break this problem into two subproblems by setting (x + 1.3) equal to 1.757839583 and -1.757839583.Subproblem 1
x + 1.3 = 1.757839583 Simplifying x + 1.3 = 1.757839583 Reorder the terms: 1.3 + x = 1.757839583 Solving 1.3 + x = 1.757839583 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.3' to each side of the equation. 1.3 + -1.3 + x = 1.757839583 + -1.3 Combine like terms: 1.3 + -1.3 = 0.0 0.0 + x = 1.757839583 + -1.3 x = 1.757839583 + -1.3 Combine like terms: 1.757839583 + -1.3 = 0.457839583 x = 0.457839583 Simplifying x = 0.457839583Subproblem 2
x + 1.3 = -1.757839583 Simplifying x + 1.3 = -1.757839583 Reorder the terms: 1.3 + x = -1.757839583 Solving 1.3 + x = -1.757839583 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.3' to each side of the equation. 1.3 + -1.3 + x = -1.757839583 + -1.3 Combine like terms: 1.3 + -1.3 = 0.0 0.0 + x = -1.757839583 + -1.3 x = -1.757839583 + -1.3 Combine like terms: -1.757839583 + -1.3 = -3.057839583 x = -3.057839583 Simplifying x = -3.057839583Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.457839583, -3.057839583}
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